{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style='color:blue' align=\"center\">Logistic Regression: Multiclass Classification</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we will see how to use logistic regression for multiclass classification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x244baced518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x244baced4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x244baa30b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x244ba4f1f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\no2BSMaynAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x244ba614b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x244ba6b3080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.gray() \n",
    "for i in range(5):\n",
    "    plt.matshow(digits.images[i]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['DESCR', 'data', 'images', 'target', 'target_names']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.,   0.,   5.,  13.,   9.,   1.,   0.,   0.,   0.,   0.,  13.,\n",
       "        15.,  10.,  15.,   5.,   0.,   0.,   3.,  15.,   2.,   0.,  11.,\n",
       "         8.,   0.,   0.,   4.,  12.,   0.,   0.,   8.,   8.,   0.,   0.,\n",
       "         5.,   8.,   0.,   0.,   9.,   8.,   0.,   0.,   4.,  11.,   0.,\n",
       "         1.,  12.,   7.,   0.,   0.,   2.,  14.,   5.,  10.,  12.,   0.,\n",
       "         0.,   0.,   0.,   6.,  13.,  10.,   0.,   0.,   0.])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style='color:purple'>Create and train logistic regression model</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(digits.data,digits.target, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style='color:purple'>Measure accuracy of our model</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.93333333333333335"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(digits.data[0:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style='color:purple'>Confusion Matrix</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_predicted = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[31,  0,  0,  0,  0,  1,  0,  0,  0,  0],\n",
       "       [ 0, 47,  0,  0,  0,  0,  0,  0,  1,  0],\n",
       "       [ 0,  0, 34,  1,  0,  0,  0,  0,  1,  0],\n",
       "       [ 0,  0,  0, 35,  0,  0,  0,  1,  4,  2],\n",
       "       [ 0,  2,  0,  0, 29,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  1,  0, 32,  0,  1,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0, 41,  0,  1,  0],\n",
       "       [ 0,  0,  0,  1,  0,  0,  0, 32,  0,  1],\n",
       "       [ 0,  4,  0,  0,  0,  0,  0,  0, 29,  0],\n",
       "       [ 0,  0,  0,  1,  1,  0,  0,  0,  0, 26]], dtype=int64)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(y_test, y_predicted)\n",
    "cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(69,0.5,'Truth')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N7G7gT+09kYiIiBSXQm1Al51ykvNk7t6/Lcdqy3LonQ2g6YKLIiIiIgXVlqtD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\n3bDkZmbdgN8CF7n7O3HnaY27Z9z9cJp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x244bae534a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sn\n",
    "plt.figure(figsize = (10,7))\n",
    "sn.heatmap(cm, annot=True)\n",
    "plt.xlabel('Predicted')\n",
    "plt.ylabel('Truth')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use sklearn.datasets iris flower dataset to train your model using logistic regression. You need to figure out accuracy \n",
    "of your model and use that to predict different samples in your test dataset. In iris dataset there are 150 samples containing following features,\n",
    "\n",
    "1. Sepal Length\n",
    "2. Sepal Width \n",
    "3. Petal Length \n",
    "4. Petal Width\n",
    "\n",
    "Using above 4 features you will clasify a flower in one of the three categories,\n",
    "\n",
    "1. Setosa\n",
    "2. Versicolour\n",
    "3. Virginica"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img height=300 width=300 src=\"iris_petal_sepal.png\" />"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
